Analytical and numerical investigation of site response due to vertical ground motion

Abstract

Due to the repeatedly observed strong vertical ground motions and compressional damage of engineering structures in recent earthquakes, the multidirectional site response analysis is increasingly critical for the seismic design of important structures, such as nuclear power plants and high earth dams. However, the site response to the vertical component of the ground motion has not been the subject of detailed investigation in the literature. Therefore, in this paper, the vertical site response due to vertical ground motion is investigated by employing both analytical and numerical methods. Firstly, a 1-D frequency domain analytical solution, which can be employed for vertical site response analysis in practice, is studied and compared against time domain Finite Element (FE) analyses for the two extreme soil state conditions (i.e. undrained and drained conditions). The vertical site response is further investigated with hydro-mechanically (HM) coupled FE analysis, considering solid-fluid interaction. The undertaken parametric studies show that the predicted vertical site response is strongly affected by the parameters characterising the hydraulic phase, i.e. soil permeability and soil state conditions, both in terms of frequency content and amplification. The subsequent corresponding quantitative investigation, of the frequency content and amplification function of the vertical site response, shows that depending on the soil permeability the response is dominated by the two types of compressional waves (fast and slow wave). Notably, the parametric studies identify a range of permeability that significantly affects dynamic soil properties in terms of P-wave velocities, damping ratios and vertical site response, and this range is relevant for geotechnical earthquake engineering applications. It is therefore recommended that coupled consolidation analysis is necessary to accurately simulate this effect at such permeability-dependent intermediate transient states between fully undrained and drained conditions. Finally, this work suggests a simple modification of standard total-stress site response analysis to account for vertical ground motion and solid-pore fluid interaction. In order to simulate the attenuation of the response due to solid-pore fluid interaction effects, it is suggested to employ additional HM viscous damping in total-stress analysis, further to the one used to account for hysteretic material damping. This additional viscous damping can be quantified based on the empirical curves proposed in the paper.

A novel insight into vertical ground motion modelling in earthquake engineering

“…The existence of one single longitudinal wave is obviously in contrast with Biot's equations, in which the propagation of two longitudinal waves is predicted within the range of high permeabilities or short propagation lengths. Moreover, the existence of one single longitudinal wave as evaluated from – formulation is in contrast with numerical findings by Han et al 33 …”

“…A parametric study is performed by considering different permeability and porosity levels, different length values of the soil column (i.e., different depth values of the bedrock, always keeping the element size constant), and different ground motions. In particular, the Christchurch earthquake (2011, New Zealand) 33 is considered in the first set of simulations, then three additional real earthquakes data are employed to investigate the response of the – and of the – formulations, namely the earthquakes of L'Aquila (2009, Italy), Emilia (2012, Italy), and Norcia (2016, Italy) 8 . The time step of the simulation is chosen equal to s. This value provides a good compromise between the computing time required by each numerical simulation and the accuracy of the solution.…”

A case study of liquefaction: demonstrating the application of an advanced model and understanding the pitfalls of the simplified procedure

“…The deconvolution of the records was carried out with the frequency domain program EERA (Bardet et al, 2000). Han (2014) and Han et al (2018) showed that this can be employed for the vertical propagation of compressional waves, in a similar fashion to Swaves.…”

Earthquake Geotechnical Engineering for Protection and Development of Environment and Constructions

“…The In the second case study, the soil column has a length of 15 m and is discretised with 30 elements; the top surface of the soil column is free, and the fluid pressure is equal to zero, as shown in figure 1b. A prescribed longitudinal displacement is applied at the bottom surface, which represents the vertical component of the Christchurch earthquake (2011, NZ) (Han & al., 2018). No water flux is allowed at the bottom and at the lateral surfaces.…”